Control charts for the Pareto distribution

The Pareto distribution plays an important role in various areas of researchIn this paper, the average run length(ARL) unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are knownThe effects of parameter estimation on the performance of the proposed control charts are also studiedResults show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARL0, which consider the variability of the parameter estimates, are further developedThe performance of the proposed control charts is investigated in terms of the ARLFinally, an example is given to illustrate the proposed control charts.     

The efficiency of CUSUM schemes for monitoring the coefficient of variation

Continuous surveillance of the coefficient of variation is a quality control issue worthy of consideration in several manufacturing and service‐oriented companies. In this paper, we present a new method to monitor the squared coefficient of variation by means of two one‐sided cumulative sum‐type control charts. We study the run length properties of the proposed charts using a Markov chain approach. Several tables are given in order to show the sensitivity of the proposed charts for different deterministic shift sizes and their performance for the random shift size condition. The results show that the proposed control charts have attractive performance compared with some competing charts and are better in many cases. An illustrative example is discussed on a real dataset. Copyright © 2016 John Wiley & Sons, Ltd.     

Distribution-free monitoring of univariate processes

We consider statistical process control (SPC) of univariate processes when observed data are not normally distributed. Most existing SPC procedures are based on the normality assumption. In the literature, it has been demonstrated that their performance is unreliable in cases when they are used for monitoring non-normal processes. To overcome this limitation, we propose two SPC control charts for applications when the process data are not normal, and compare them with the traditional CUSUM chart and two recent distribution-free control charts. Some empirical guidelines are provided for practitioners to choose a proper control chart for a specific application with non-normal data.     

一个监控方差的与分布无关的变点模型

文献中绝大部分与分布无关的控制图用于监控过程位置参数,如均值或中位数,而非过程方差.该文开发了一个新的与分布无关的控制图,通过整合一个两样本非参数检验和有效的变点模型.所提出的控制图容易计算,方便应用,并且对于探测过程方差的漂移非常有效.因为它避免了在监控之前的一个很长时间的收集数据的阶段,并且它不需要潜在的过程分布的知识,因此,所提出的控制图在开始阶段或者短程运行情况下特别有用.     

Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance

In statistical process control (SPC), when dealing with a quality characteristic x that is a variable, it is usually necessary to monitor both the mean value and variability. This article proposes an optimization algorithm (called the holistic algorithm) to design the CUSUM charts for this purpose. It facilitates the determination of the charting parameters of the CUSUM charts and considerably or significantly increases their overall detection effectiveness. A single CUSUM chart (called the ABS CUSUM chart) has been developed by the holistic algorithm and fully investigated. This chart is able to detect two-sided mean shifts and increasing variance shifts by inspecting the absolute value of sample mean shift. The results of performance studies show that the overall performance of the ABS CUSUM chart is nearly as good as an optimal 3-CUSUM scheme (a scheme incorporating three individual CUSUM charts). However, since the ABS CUSUM chart is easier for implementation and design, it may be more suitable for many SPC applications in which both mean and variance of a variable have to be monitored.     

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.     

联合监测过程位置参数和尺度参数的非参数Shewhart控制图

用于检测生产服务过程的传统控制图多数都假定过程的分布是已知的。这些控制困经常是在正态分布的假设下构建的,然而在服务质量实时监控中数据往往是非正态的。在这种情况下,基于正态分布假设的控制图的结果是不可靠的。为了解决这个问题,通常考虑非参数方法,因为在过程分布未知情况下,非参数控制图比参数图更加稳健有效。本文提出一个新的基于Van der Waerden和Klotz检验的Lepage型非参数Shewhart控制图(称为LPN图)用于同时检测未知连续过程分布的位置参数和尺度参数。文中给出了LPN图在不同参数下的控制限。依据运行长度分布的均值,方差和分位数,分析了LPN图在过程受控和失控时的性能,并与其他一些现有的非参数控制图进行比较。基于蒙特卡洛的模拟结果表明,LPN图对非正态分布具有很好的稳健性,并且在不同的过程分布下对检测位置参数和尺度参数,尤其对检测尺度参数的漂移都具有很好的性能。最后通过监控出租车服务质量说明LPN图在实际中的应用。     

Statistical process control for monitoring scheduling performance—addressing the problem of correlated data

In both manufacturing and service operations effective scheduling plays an important role in achieving delivery performance and in utilizing resources economically. Classical scheduling theory takes a narrow, static view of performance. In reality the assessment of scheduling performance is a particularly difficult task. Typically scheduling is an activity that takes place repeatedly over time in the context of an overall planning and control architecture. Scheduling may be viewed as an activity within a process. Statistical Process Control (SPC) provides an attractive option for monitoring performance. In this paper we investigate the potential of applying SPC control charts in this context. The feasibility of monitoring flow time in a single processor model using control charts is studied using simulation. The application of control charts to monitor time-related measures in operational systems raises fundamental statistical problems. The need for approaches that are robust with respect to data correlation and lack of normality is shown to be an essential requirement. Residual-based approaches and the Exponentially Weighted Moving Average (EWMA) chart are shown to be reasonably effective in avoiding false alarms and in detecting process shifts. The applicability of the single processor model to more complex operational systems is discussed. The implications of the work for the design of performance monitoring and continuous improvement systems for time-related measures in manufacturing and service operations are considered. A number of areas are highlighted for further theoretical and practical studies.     

A new multivariate variability control chart based on a covariance matrix combination

In the field of multivariate quality control, there are many control charts related to the process mean but few options addressing process variability. Variability control charts have two main drawbacks: the first relates to the number of parameters to tune and the second relates to how changes in the mean affect the performance of these charts. Thus, in this paper, we propose a new multivariate variability control chart, called the multivariate exponentially weighted covariance matrix combination, which solves these two problems. The results show that this new chart performs well in the detection of changes in variance when the mean does not change and outperforms other charts when the mean does change.     

监测Lévy稳定过程均值变点的平均运行时间估计

平均运行长度(时间)(ARL)是判断一控制图监测变点效果好坏的一个重要工具.本文主要研究Lévy稳定过程的均值变点监测问题.我们给出了三个控制图,即EWMA,GEWMA和GLR的ARL估计,并通过数值模拟比较了4个控制图监测均值变点的效果和差异.